That means Tuesday is the day that Republicans will start reaping the benefits of the once-in-a-decade redistricting process. Because of their big gains in the 2010 elections, Republicans control the legislature and governor’s mansion in so many states that they got to redraw four times as many congressional districts as Democrats.

But just how much of an advantage did they really have?

To answer that question, The Fix reviewed the 66 districts that Republicans won from Democrats last year.

A look at the changes to those 66 districts in this round of redistricting shows that Republicans do indeed come out of redistricting with a better map than they had before.

But the improvements in a lot of cases were slight, and most Republicans who were vulnerable before will continue to be at risk over the next decade.

First, though, a recap of how we got to this point:

We’ve written before on this blog about how, despite the GOP’s unprecedented control over the drawing of new lines, its big majority makes creating new seats for the party to win much more difficult.

In other words, because Republicans control more seats than they have at any point in the past 60 years, and because they hold the vast majority of competitive districts already, it was much harder to create new districts that they could win.

(There’s only so much you can do, given the demographics of a state and the rules involved, including equal population, protection of minority voting rights and standards for compactness, etc.)

And so far, Republicans and Democrats have come out pretty much even when it comes to creating new districts they can win in the 2012 election.

But that’s only one part of the equation.

The other part is where the GOP’s real advantage lies: improving on the districts it already controls, a.k.a. “shoring up” its incumbents.

Ohio is a good example of this. Republicans already control 13 of 18 congressional seats in a swing state, and with the state losing two seats thanks to population shifts, they had to pack as many Democrats into as few districts as possible in order to protect their members. In the end, they created four Democratic districts and did their best to shore up the remaining 12 GOP-held districts.

The result was that each party is likely to lose one seat.

And while on the surface that looks like a wash, Republicans were able to use their advantage to make three of their most vulnerable members much safer. And that gives them a significantly better shot at holding on to their majority for the next five election cycles.

Two of the beneficiaries — freshman Reps. Steve Stivers and Steve Chabot — each won districts in 2010 where Sen. John McCain (R-Ariz.) had taken just 45 percent of the vote in the 2008 presidential race. Chabot’s new district, though, would have given McCain about 52 percent, while Stivers’s would have given him 53 percent.

“This is my first reelection campaign and I am taking this race as seriously as I did in 2008 and 2010, when the district was one of the most competitive in the nation,” Stivers said.

Stivers, despite his careful approach, got one of the biggest bumps in the country thanks to redistricting. In other words: Results not typical.

In fact, compared to the 65 other Republican freshmen who won Democratic seats in 2010, Stivers got the fifth-biggest overall improvement.

Here’s how it breaks down:

* Republicans got to redraw 37 of the 66 districts where Republican freshmen won Democratic seats, while Democrats got to redraw nine.

* Of the 66 districts, eight haven’t yet been redrawn and two are at-large districts — i.e. they can’t be redrawn because the districts cover the whole state.

* Of the 56 districts that have been redrawn, more than half (32) have been redrawn to become more Republican-friendly, 14 districts got more difficult for Republicans, and the remaining 10 districts will be basically the same as they are now.

* A further breakdown shows that while most of the districts will become better for the GOP, the difference is often pretty small. Of the 32 districts that become more Republican, about half (15) will become only 1 percent or 2 percent more Republican, and only 10 will become at least 5 percent more Republican. (Similarly, more than half of the districts that become more Democratic will be only a point or two bluer.)

In the end, 35 of the 56 districts will change by two points or less — a strong sign that these Republicans will continue to have to watch their backs in the coming election, even if most of them are safer.

“If you sum all this up, I think it supports the case that the Republican plan to shore up freshmen reaped only minor gains, and may have been too conservative, given their control of the process,” said Democratic redistricting guru Mark Gersh.

A few caveats here:

One is that we’re looking only at freshmen who won Democratic districts and not all vulnerable Republicans. (At the same time, these freshmen represent most of the Democrats’ top targets in 2012.)

Second, not all of these members are vulnerable. Despite all of these districts being held by a Democrat just more than a year ago, a few of them were very conservative districts where it seemed to be only a matter of time before Republicans won them and locked them down. Democrats really weren’t planning to target freshmen such as Rep. Bill Flores (R-Texas), whose district got about 8 points bluer but remains very conservative, or Rep. Raul Labrador (R-Idaho), whose district stayed about the same.

Last, this review is based on the districts as they stand now. Court challenges could still affect the districts in states like Florida and Texas. Stayed tuned to The Fix for all the latest on that.

Regardless of what happens from here on out, though, the overall picture is starting to come into focus.

And that picture is this: The map with which Republicans have to protect their majority in 2012 will be more GOP-friendly — though not significantly so — than the map with which they won the majority in 2010.